Static And Dynamical Properties Of Classical Two-dimensional Clusters

This thesis is devoted to theoretical research of classical Wigner crystal lattice. The pupose of the research is to reveal in detail the structural, dynamical and melting properties of a finite size classical Wigner crystal. And the influence of impurity and different types of hard wall potential to system ground-state configuration and dynamics is investigated.Most of the work in this thesis is motivated by experimental results. In the first chapter, I give a few specific examples of experimental systems which have been realized to investigate the Wigner crystal.The second chapter of the thesis gives a description of the model system and the corresponding numerical approach. An improvement has been made to the previous method Comparing with the old one, our new algorithm can calculate large-scale systems (N>500), especially those under different hard-wall potential, e.g. ellipse and rectangle, without reducing the precision.In the third chapter we discuss the influence of ellipse and rectangle hard-wall potential on classical Wigner lattice. In the case of square boundary, it is interesting to notice that when N is greater than 66, inner particles become the hexagon lattice is. But for parabolic and circular hard-wall confinement potential, there is no hexagon Wigner crystal lattice until N>100 and 300, respectively.The effect of impurity on classical Wigner crystal lattice is investigated in the fourth chapter. An overall discussion is dedicated to the ground-state configuration and melting behavior of a system with impurity.The dynamical matrices of classical particles in their equilibrium under Cartesian and ellipse coordinate are deduced. Then we make a detailed comparison between normal modes under circular hard-wall and parabolic confinement potential. Finally, the influence of ellipse boundary on the normal mode of a small-scale system is analyzed.